论文信息 - Fixed Point Problems on Generalized Metric Spaces in Perov's Sense

Fixed Point Problems on Generalized Metric Spaces in Perov's Sense

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov’s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results.

[1] Xian Zhang,et al. Cone metric spaces and fixed point theorems of contractive mappings , 2007 .

[2] Abdul Latif,et al. Fixed Point Results for Generalized Contractive Multimaps in Metric Spaces , 2009 .

[3] Dorian Popa,et al. The Hyers–Ulam stability of nonlinear recurrences , 2007 .

[4] Ulam-Hyers Stability for Operatorial Equations , 2011 .

[5] J. Brzdȩk,et al. Hyers-Ulam stability for linear equations of higher orders , 2008 .

[6] Adrian Petruşel,et al. Data dependence of the fixed point set of some multivalued weakly Picard operators , 2003 .

[7] Wataru Takahashi,et al. Fixed point theorems and characterizations of metric completeness , 1996 .

[8] G. E. Hardy,et al. A Generalization of a Fixed Point Theorem of Reich , 1973, Canadian Mathematical Bulletin.

[9] J.-C. Yao,et al. ULAM-HYERS STABILITY FOR OPERATORIAL EQUATIONS AND INCLUSIONS VIA NONSELF OPERATORS , 2011 .

[10] D. O’Regan,et al. Continuation Theory for Contractions on Spaces with Two Vector-Valued Metrics , 2003 .

[11] D. H. Hyers. On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[12] Multivalued generalized nonlinear contractive maps and fixed points , 2011 .

[13] V. Lazăr. Ulam-Hyers stability for partial differential inclusions , 2012 .

[14] P. P. Zabrejko. K-metric and K-normed linear spaces: survey. , 1997 .